Pipe Pressure Drop (Darcy-Weisbach)
Friction loss in a round pipe — Swamee-Jain friction factor, automatic laminar branch.
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The engineering
Darcy-Weisbach is the honest pipe-friction law: loss scales with length over diameter times the velocity head, and all the mess of turbulence hides in f. This card gets f from the Swamee-Jain fit to the Colebrook equation — within about 1% over the practical range, no iteration — and switches to the exact laminar 64/Re when Re drops below 2,300.
The velocity-squared term is where pipe systems are won or lost: bumping a line one nominal size typically cuts velocity ~40% and pressure drop by more than half. If your head loss looks absurd, check the diameter before you doubt the pump.
Where this math comes from
Julius Weisbach put the equation in its modern f·(L/D)·V²/2g form in 1845; Henry Darcy's meticulous experiments on the Dijon water supply (published 1857) showed the factor depends on the pipe wall, not just the fluid — roughness enters engineering. The two never collaborated, but the hyphen stuck.
The friction factor itself took another century to tame: Colebrook and White fused the smooth and rough limits into one implicit formula in 1939, Lewis Moody plotted it as the famous chart in 1944, and Swamee and Jain's 1976 explicit fit finally let a calculator — this one — skip the iteration.
- 1845Julius WeisbachModern head-loss equation with f.
- 1857Henry DarcyDijon experiments make roughness part of the law.
- 1939Cyril ColebrookImplicit transition formula for f.
- 1944Lewis MoodyThe Moody chart — f at a glance.
- 1976P. K. Swamee & A. K. JainExplicit f formula — the one this card evaluates.
See the full timeline of the math behind every calculator →
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